Three Roads To Quantum Gravity

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BLACK HOLES ARE HOT 93 seems to be a contradiction, but if so we must explain how the information gets out, as it is coded in photons that are trapped behind the horizon. Similarly, we can also ask whether the entropy of the black hole decreases as the area of the horizon shrinks. It seems that it must, as the two quantities are related. But surely this violates the second law of thermodynamics, which states that entropy can never decrease? One answer is that it need not, because the radiation emitted by the black hole has lots of entropy, which makes up for that lost by the black hole. The second law of thermodynamics requires only that the total entropy of the world never increase. If we include in this total the entropy of the black hole, then all the evidence we have is that the second law of thermodynamics still holds. When something falls into a black hole the outside world may lose some entropy, but the increase in the entropy of the black hole will more than make up for it. On the other hand, if the black hole radiates it loses surface area and hence entropy, but the entropy of the outside world will increase to make up for it. The result of all this is at the same time very satisfying and deeply puzzling. It is satisfying because the study of black holes has led to a beautiful extension of the laws of thermodynamics. It seemed at ®rst that black holes would violate the laws of thermodynamics. But eventually we realized that if black holes themselves have entropy and temperature, then the laws of thermodynamics would remain true. What is puzzling is that in most circumstances entropy is a measure of missing information. In classical general relativity a black hole is not something complicated: it is described by a few numbers such as its mass and electric charge. But if it has entropy there must be some missing information. The classical theory of black holes gives us no clue as to what that information is about. Nor do the calculations by Bekenstein, Hawking and Unruh give us any hint about what it might be. But if there is no clue from the classical theory as to the nature of the missing information, there is only one possibility, which is that we need the quantum theory of a black hole to reveal it to us. If we could understand a black hole as a
94 THREE ROADS TO QUANTUM GRAVITY purely quantum system, then its entropy would have to turn out to include some information about itself that is evident only at the quantum level. So we may now pose a question which could be answered only if we have a quantum theory of gravity. What is the nature of the information trapped in a quantum black hole? Keep this in mind as we go ahead and explore the different approaches to quantum gravity, for a good test of a theory of quantum gravity is how well it is able to answer this question.
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CHAPTER 2 .........................
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CHAPTER 11 ........................
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CHAPTER 12 ........................
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THE HOLOGRAPHIC PRINCIPLE 171 gener
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THE HOLOGRAPHIC PRINCIPLE 173 FIGUR
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THE HOLOGRAPHIC PRINCIPLE 175 the g
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THE HOLOGRAPHIC PRINCIPLE 177 In th
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CHAPTER 13 ........................
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HOW TO WEAVE A STRING 181 thing!" I
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HOW TO WEAVE A STRING 183 other. Th
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HOW TO WEAVE A STRING 185 What is r
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HOW TO WEAVE A STRING 187 for a pic
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HOW TO WEAVE A STRING 189 in Einste
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HOW TO WEAVE A STRING 191 p in the
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HOW TO WEAVE A STRING 193 may be th
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WHAT CHOOSES THE LAWS OF NATURE? 19
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EPILOGUE: .........................
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EPILOGUE: 209 And quantum gravity i
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EPILOGUE: 211 of systems containing
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POSTSCRIPT 213 These cosmic rays ar
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POSTSCRIPT 215 Three explanations h
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POSTSCRIPT 217 light, which is the
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POSTSCRIPT 219 This is good news in
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POSTSCRIPT 221 But there is a secon
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POSTSCRIPT 223 Chopin Soo and Marti
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POSTSCRIPT 225 speed of light with
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GLOSSARY 227 cannot be greater than
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GLOSSARY 229 event In relativity th
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GLOSSARY 231 Newton's gravitational
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GLOSSARY 233 spin The angular momen
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SUGGESTIONS FOR FURTHER READING ...
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INDEX .............................
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INDEX 243 black hole, 70, 73±4, 17
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INDEX 245 black hole formation, 189
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Three Roads To Quantum Gravity

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